Theoretically, using a result of hashing as password means enough security for anyone for eternity. That’s the whole point in hashing, it creates a random but (up to a limit) unique string so you only have to remember a shorter phrase. Given the enormous number of possibilities it is virtually impossible to bruteforce a hash of a hash or even find in a rainbow table.
I am personally using the same technique and see no flaw of it, so I can confidently recommend it to anyone. Just remember which algorithm you used.